Using the variance function to generalize Bland-Altman analysis

Bland-Altman analysis is a popular and widely used method for assessing the level of agreement between two analytical methods. An important assumption is that paired method differences exhibit approximately constant (homogeneous) scatter when plotted against pair means. This allows estimation of limits of agreement which retain validity across the entire range of mean values. In practice, pair differences often increase systematically with the mean and Bland and Altman used log transformed data to achieve approximately homogeneous scatter. Unfortunately, a logarithmic transformation fails when data are located near the detection limit of an assay (a region that is often of considerable clinical importance).

Simulated thyrotropin data are used to illustrate how a variance function, estimated from pair differences, can be used to transform problematic data into a form suitable for traditional Bland-Altman analysis. Simulated and real data sets are used in a supplementary file to illustrate and offer practical solutions to potential problems.

Following transformation by variance function, Bland-Altman results can be readily interpreted by back-transformation either to the original measurement scale or as percentage values. Limits of agreement are no longer horizontal straight lines, but their shapes simply reflect error characteristics which are (or should be) thoroughly familiar to laboratory analysts.

The method is completely general and in principle requires only the estimation of a variance function that reliably describes the relationship between the variances of pair differences and their mean values. A computer program is available which performs the necessary calculations.